Volume 65, Issue 1
July 2005, pages 1-164
pp 1-15 July 2005
The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials
The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis onhigher excited states andstronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials withn <- 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high asn = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. Then > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.
pp 17-33 July 2005
Stability of naked singularity arising in gravitational collapse of Type I matter fields
Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary C^{2}-mass functionM(r, v) and a C^{1}-functionh(r, v) (through the corresponding C^{1}-metric functionν(t, r)), there exist infinitely many choices of energy distribution functionb(r) such that the ’true’ initial data(M, h(r,v)) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a ’big’ subset of the true initial data set, their occurrence is not generic. The terms ’stability’ and ’genericity’ are appropriately defined following the theory of dynamical systems. The particular case of radial pressurep_{r}(r) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.
pp 35-41 July 2005
Charged fluid distribution in higher dimensional spheroidal space-time
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
pp 43-48 July 2005
Collineations of the curvature tensor in general relativity
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
pp 49-59 July 2005
Supersymmetric quantum mechanics for two-dimensional disk
Akira Suzuki Ranabir Dutt Rajat K Bhaduri
The infinite square well potential in one dimension has a smooth supersymmetric partner potential which is shape invariant. In this paper, we study the generalization of this to two dimensions by constructing the supersymmetric partner of the disk billiard. We find that the property of shape invariance is lost in this case. Nevertheless, the WKB results are significantly improved when SWKB calculations are performed with the square of the superpotential. We also study the effect of inserting a singular flux line through the center of the disk.
pp 61-74 July 2005
Anasuya Kundu Barnali Chakrabarti Tapan Kumar Das
We adopt the potential harmonics expansion method for anab initio solution of the many-body system in a Bose condensate containing interacting bosons. Unlike commonly adopted mean-field theories, our method is capable of handling two-body correlation properly. We disregard three- and higher-body correlations. This simplification is ideally suited to dilute Bose Einstein condensates, whose number density is required to be so small that the interparticle separation is much larger than the range of two-body interaction to avoid three- and higher-body collisions, leading to the formation of molecules and consequent instability of the condensate. In our method we can incorporate realistic finite range interactions. We calculate energies of low-lying states of a condensate containing^{23}Na atoms and some thermodynamical properties of the condensate.
pp 75-84 July 2005
Fine-structure energy levels, oscillator strengths and lifetimes of chlorine-like chromium
Man Mohan Avnindra K Singh Alok K S Jha Narendra Singh
We have done relativistic calculations for the evaluation of energy levels, oscillator strengths, transition probabilities and lifetimes for Cr VIII ion. Use has been made of configuration interaction technique by including Briet-Pauli approximation. The energies of various levels from the ground state to excited levels of 3s3p^{6}, 3s^{2}3p^{4}3d, 3s^{2}3p^{4}4s, 3s^{2}3p^{4}4d of Cr VIII are given in LSJ coupling scheme after fine-tuning and are compared with the experimental results compiled in the NIST Data Base. Many new lines have been predicted which have not appeared so far in the NIST Data.
pp 85-93 July 2005
Quasi-binary incident electron—centre of mass collision in (e, 3e) process on He and He-like ions
We present in this communication the results of our first Born calculation in the three-Coulomb (3C) wave approach for the (e, 3e) process on He and He-like ions at an incident electron energy 5599 eV in the coplanar constant θ12 as well as out-of-plane constant φ12 modes. These two geometrical modes are such that the quasi-binary collision between the incident electron and centre of mass of the ejected electrons is in the scattering plane. The theoretical formalism has been developed using plane waves, Le Sech wave function and approximated BBK-type wave function respectively for the incident and scattered, bound and ejected electrons to calculate five-fold differential crosssection (FDCS) of the (e, 3e) process. We emphasize on the similarities and dissimilarities (asymmetries) in the angular profile of the FDCS in two modes as well as the effects of post-collision interaction (between the ejected electrons) and nuclear chargeZ on the angular profile of the FDCS. We observe that with the increment of nuclear charge the two quasi-binary collisions approach towards identical behaviour at larger mutual angles and thus bringing less asymmetry in FDCS for higherZ target.
pp 95-105 July 2005
Fiber lasers have attracted considerable attention when their power can realistically be scaled to kilowatt level and beyond. In this paper, we assumed that the fiber core and first clad are exposed to a pump source with a super-Gaussian profile of order four. The effects of this non-uniform heat deposition on thermal, stress and thermooptics properties such as temperature-dependent change of refractive index and thermally induced stress have been comprehensively studied and their equations analytically derived.
pp 107-116 July 2005
The constancy of the contact angle in viscous liquid motions with pinned contact lines
Consider motion initiated in a viscous liquid in a smooth walled container. The liquid is initially at rest under uniform pressure from an inert gas of negligible inertia. We show that if the contact line is pinned and the interface is single valued, the contact angle has to remain constant throughout the motion. This is true even for motions of finite amplitude. Some implications of the result are discussed.
pp 117-124 July 2005
The Bohm criterion for a dusty plasma sheath
The formation of the sheath in a dusty plasma is investigated. The Bohm criterion is derived for two different cases: (a) when electrons are in thermodynamic equilibrium and dust grains provide the immobile, stationary background and (b) when both electrons and ions are in thermodynamic equilibrium and dust grains are moving. In the first case, Bohm criterion gets modified due to the fluctuation of the charge on the grain surface. In the second case, the collisional and Coulombic drag play important role in determining the Bohm criterion.
pp 125-135 July 2005
An effective pair potential for liquid semiconductor, Se: Structure and related dynamical properties
The effective pair potential of liquid semiconductor Se is extracted from its experimental structure factor data using an accurate liquid state theory and this shows important basic features. A model potential incorporating the basic features of the structure factor extracted potential is suggested. This model potential is then used to describe through low-order perturbation theory, the structure and related dynamical properties like self-diffusion coefficient and shear viscosity of this complex liquid over a wide range of temperatures.
pp 137-145 July 2005
Performance of 20 Ci^{137}Cs γ-ray Compton spectrometer for the study of momentum densities
In this paper, we present the design and construction of a 20 Ci γ-ray Compton spectrometer that employs a^{137} Cs source with a strong line at 661.65 keV. The total resolution of the spectrometer in momentum scale is 0.40 a.u., which is much better than the conventional^{241}Am Compton spectrometers. The in-house^{137}Cs spectrometer is very useful for the measurement of momentum densities of heavy materials. The performance of the machine is assessed using aluminum, terbium and mercury samples and the experimental data from comparable apparatus.
pp 147-152 July 2005
Semi-classical limit of relativistic quantum mechanics
It is shown that the semi-classical limit of solutions to the Klein-Gordon equation gives the particle probability density that is in direct proportion to the inverse of the particle velocity. It is also shown that in the case of the Dirac equation a different result is obtained.
pp 153-157 July 2005
Absorption spectrum of Mn^{2+} ions doped in diammonium hexaaquamagnesium(II) sulfate
Ram Kripal Ashutosh Kumar Shukla
Optical absorption is a tool to investigate the site symmetry of metal ion and associated distortion in doped single crystals. It provides the energy of different orbital levels of metal ion and separation among them. Mn^{2+} ions in various single crystals and glasses have been the subject of recent investigations [1–3]. We have studied optical absorption spectra of Mn^{2+} doped diammonium hexaaquamagnesium(II) sulfate in order to obtain the energy level ordering using matrices of Tanabe and Sugano [4] and to discuss the associated distortion.
pp 159-164 July 2005
On the bremsstrahlung background correction to the high-energy Compton spectroscopy
methodology for bremsstrahlung (BS) background correction to extract a true Compton profile in high-energy Compton scattering experiments is presented. The BS background profiles for Hg, computed within the Born approximation, are estimated for different values of incident energy. It is seen for the first time that the BS background contribution in high-energy Compton profile experiments like those employing third generation synchrotron radiation sources comes out to be significant and non-linear. Further, it is found that the incorporation of BS correction in data reduction of such an experiment performed on Hg at 662 keV energy helps in reconciliation of theory and experiment.
Current Issue
Volume 93 | Issue 5
November 2019
Click here for Editorial Note on CAP Mode
© 2017-2019 Indian Academy of Sciences, Bengaluru.